How Euler would compute the Euler-Poincar\'e characteristic of a Lie superalgebra
K-Theory and Homology
2012-01-30 v3 Classical Analysis and ODEs
Rings and Algebras
Abstract
The Euler-Poincar\'e characteristic of a finite-dimensional Lie algebra vanishes. If we want to extend this result to Lie superalgebras, we should deal with infinite sums. We observe that a suitable method of summation, which goes back to Euler, allows to do that, to a certain degree. The mathematics behind it is simple, we just glue the pieces of elementary homological algebra, first-year calculus and pedestrian combinatorics together, and present them in a (hopefully) coherent manner.
Cite
@article{arxiv.0812.2255,
title = {How Euler would compute the Euler-Poincar\'e characteristic of a Lie superalgebra},
author = {Pasha Zusmanovich},
journal= {arXiv preprint arXiv:0812.2255},
year = {2012}
}
Comments
v3: minor English corrections